ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 12 Jun 2012 05:47:52 -0500Polynomial representation of GF(7)?http://ask.sagemath.org/question/9061/polynomial-representation-of-gf7/Why sage would give me polynomial representation of GF(8), but not GF(7)?
sage: G = GF(8, 'x')
sage: G.list()
[0, x, x^2, x + 1, x^2 + x, x^2 + x + 1, x^2 + 1, 1]
sage: G = GF(7, 'x')
sage: G.list()
[0, 1, 2, 3, 4, 5, 6]
Maybe there's no such thing as polynomial represenation of GF(7)?Tue, 12 Jun 2012 03:38:30 -0500http://ask.sagemath.org/question/9061/polynomial-representation-of-gf7/Answer by calc314 for <p>Why sage would give me polynomial representation of GF(8), but not GF(7)?</p>
<pre><code>sage: G = GF(8, 'x')
sage: G.list()
[0, x, x^2, x + 1, x^2 + x, x^2 + x + 1, x^2 + 1, 1]
sage: G = GF(7, 'x')
sage: G.list()
[0, 1, 2, 3, 4, 5, 6]
</code></pre>
<p>Maybe there's no such thing as polynomial represenation of GF(7)?</p>
http://ask.sagemath.org/question/9061/polynomial-representation-of-gf7/?answer=13692#post-id-13692If $p$ is a prime, then `GF(p^n,'x')` is obtained by computing $F_p[x] / (f(x))$ where $f$ is a monic, irreducible polynomial of degree $n$ in $F_p[x]$. For $n=1$, you just get $F_p[x] / (x) \cong F_p$.
So, for any prime $p$, `GF(p,'x')` is `[0,1,2,...,p-1]`.
Tue, 12 Jun 2012 05:11:47 -0500http://ask.sagemath.org/question/9061/polynomial-representation-of-gf7/?answer=13692#post-id-13692Comment by bk322 for <p>If $p$ is a prime, then <code>GF(p^n,'x')</code> is obtained by computing $F_p[x] / (f(x))$ where $f$ is a monic, irreducible polynomial of degree $n$ in $F_p[x]$. For $n=1$, you just get $F_p[x] / (x) \cong F_p$.</p>
<p>So, for any prime $p$, <code>GF(p,'x')</code> is <code>[0,1,2,...,p-1]</code>.</p>
http://ask.sagemath.org/question/9061/polynomial-representation-of-gf7/?comment=19620#post-id-19620Oh I see - so it's just because `n=1`. Thank You for Your answer.Tue, 12 Jun 2012 05:47:52 -0500http://ask.sagemath.org/question/9061/polynomial-representation-of-gf7/?comment=19620#post-id-19620